The Prophet (sallallahu `alayhi wa-sallam) said: "A believer who mixes with the people and endures the pain they inflict, is more virtuous than one who does not mix with the people and bear that pain." [Ibn Majah, A?mad and others]
The greatest of men, the pinnacle of nobility and uprightness was himself subjected to all kinds of accusations. They called the Prophet a liar, a mad man, a soothsayer and much more. They even made false accusations against his wife. Yet he continued with his mission. We should take courage from live of the Prophet (Sallallahu `alayhi wa-sallam).
Malice scorned, puts out itself; but worrying about it and spending too much time trying to refute it, gives a kind of credit to the false accusation